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This is not Homework.l do this for fun and expand my learning.

I am obviously having difficulties with SD+,thus l post many problems.

I am using the Logic Book

Problem has be done in SD+

Using goal analysis l thought the best idea is to create a disjunction from 1 or 2 to get F. I thought Contradiction because of J is not the premises. But will try ND.

My partial attempt

Derive F =>J

1.F=>(~GvH) Assume

2.F=>G. Assume

3.~(HvI.) Assume

4.|J Assume

5.|F 2R

6.| G 5,2 =>E

7.|~F v ~~G 6 DN

8.~(F & ~G) 7 DeM

...

K-2:||-F

K-1:||-J

K :|F=>J

I request help on how to do it with

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  • 1
    The premises? 1,2,3 ? – Mauro ALLEGRANZA Mar 25 at 18:53
  • If so, assume F and derive G from 2 and H from 1. From H, derive H or I and it's done. – Mauro ALLEGRANZA Mar 25 at 18:54
  • 1-3 are the assumptions so l can assume J – Eudoxus Mar 25 at 20:38
  • 1
    Yes, you can assume whatever you want... But J is useless: you have to derive it. – Mauro ALLEGRANZA Mar 26 at 6:56
  • Since you posted many similar questions here, I think you just fail to understand how natural deduction (be it in Fitch form) is supposed to work... If understanding that rather than solving these trivial problems somewhat less formally is your goal, it's probably better you look up some solved examples, be it your book or elsewhere... Also you seldom present the problem clearly here. See e.g. Mauro's first comment. – Fizz Mar 26 at 14:38
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So, you want to prove F ->J from the premises F -> (~GvH), F -> G, ~(HvI) . The first thing to note is that since J doesn't appear in the premises, you're really saying F implies anything. That can only hold if F is false. So your first step is to show that F is false.

Assuming F, you obtain G and ~G v H. ~G v H is the same as G -> H. So, you obtain H. But you also have ~(H v I) which is the same as ~H & ~I, which gives you ~H. Now you have a contradiction. Therefore, F is false.

Knowing ~F, you obtain ~F v J which is the same as F -> J.

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  • I went through some of those derivations but didn’t get ~H Thanks – Eudoxus Mar 25 at 22:33
  • Who down voted me. What did I do to do deserve it – Eudoxus Mar 27 at 14:05

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